Development and validation of predictive nomogram for postoperative non-union of closed femoral shaft fracture

Closed femoral shaft fracture is caused by high-energy injuries, and non-union exists after operation, which can significantly damage patients’ body and mind. This study aimed to explore the factors influencing postoperative non-union of closed femoral shaft fractures and establish a predictive nomogram. Patients with closed femoral shaft fractures treated at Hebei Medical University Third Hospital between January 2015 and December 2021 were retrospectively enrolled. A total of 729 patients met the inclusion criteria; of them, those treated in 2015–2019 comprised the training cohort (n = 617), while those treated in 2020–2021 comprised the external validation cohort (n = 112). According to multivariate logistic regression analysis, complex fractures, bone defects, smoking, and postoperative infection were independent risk factors. Based on the factors, a predictive nomogram was constructed and validated. The C-indices in training and external validation cohorts were 0.818 and 0.781, respectively; and the C-index of internal validation via bootstrap resampling was 0.804. The Hosmer–Lemeshow test showed good fit of the nomogram (P > 0.05) consistent with the calibration plot results. The clinical effectiveness was best at a threshold probability of 0.10–0.40 in decision curve analysis. The risk prediction for patients with fractures using this nomogram may aid targeted prevention and rehabilitation programs.


Data collection
Through telephone follow-up and medical record review, the following research contents were collected: (i) preoperative factors: sex, age, ethnic origin, urbanization, occupation, body mass index (BMI), season, smoking, drinking, AO/OTA classification, injury cause, preoperative combined injuries, and preoperative underlying conditions (hypoalbuminemia, diabetes, hypertension, coronary heart disease, osteoporosis, respiratory system disease, hepatobiliary system disease, anemia, and others); (ii) intraoperative factors: waiting time for surgery, operation method, internal fixation, anesthesia, and bone defect; (iii) postoperative factors: postoperative complications (postoperative infection, deep vein thrombosis of the lower extremities, and others), rehabilitation training, and weight-bearing time.In this study, patients were divided into six age groups: 0-10, 11-20, 21-30, 31-40, 41-50, and > 50 years.According to AO/OTA classification 13 , the fractures were divided into types A, B, and C, corresponding to simple, wedge, and comminuted fractures, respectively.Hypoalbuminemia refers to the serum albumin level < 35 g/L 14 .Rehabilitation training means that patients with closed femoral shaft fractures were trained by the hospital's rehabilitation department or professional rehabilitation institutions outside the hospital.
All surgeries in this study were performed by equally qualified doctors, and the patients' medical record information and imaging data were collected, followed up, collated, and analyzed by trained orthopedic surgeons and radiologists.Supervision and sampling examinations were performed by a chief orthopedic physician and a chief radiologist.

Outcomes
Delayed union of fracture is defined as that X-ray shows there is a small amount of callus at the fracture site, the fracture line was clearly visible, and the broken end of the fracture was not hardened at 3-6 months after surgery 15 .Fracture non-union refers to the occurrence of broken end ossification, medullary cavity closure, pseudarthrosis and so on at 8-12 months after surgery 15 .Patients with closed femoral shaft fracture non-union or delayed union were classified as non-union cases.

Predictive model validation
Validation of the predictive model can be divided into discrimination, calibration, and clinical effectiveness.The C-index is the main index used to evaluate the discrimination of a model and is the same as the area under the receiver operating characteristic (ROC) curve in the multivariate logistic regression model.The value is 0.50-1.00,which is bounded by 0.70 and 0.90, corresponding to low, medium, and high discrimination, respectively 16 .The Hosmer-Lemeshow (H-L) test was used to calibrate the model.Values of P > 0.05 indicated a strong goodness of fit between the predicted value and the actual value of the model as well as high calibration.As a visual form of calibration, in the calibration plot, the closer the actual prediction curve is to the ideal, the higher the calibration 17 .Clinical effectiveness is generally evaluated using clinical decision curve analysis (DCA), which indicates that the prediction model can be applied to disease screening to obtain the threshold range of clinical benefit for patients 18 .

Statistical analysis
Statistical analyses were performed using R 4.3.0statistical software (R Foundation for Statistical Computing, Austria).All of the collected factors were categorical variables that were statistically described as frequency and proportion.The intergroup comparison was conducted using the χ 2 test; when the theoretical frequency of any grid in 2 × 2 crosstab was < 1 or the theoretical frequency of > 20% of the grid in R × C crosstab was < 5, Fisher's exact test was applied.A univariate analysis was performed in the training cohort to select variables with values of P < 0.05.
The variables were further analyzed using multivariate logistic regression, and independent risk factors related to postoperative non-union of closed femoral shaft fractures were identified.The α value of the test level was 0.05 on both sides.In the logistic regression analysis table, beta (B) is the regression coefficient; that is, the parameter that represents the influence of the independent variable on the dependent variable in the regression equation.The standard error (SE) is used to measure sampling error.The smaller the SE, the more reliable the inference of the population parameters from the sample statistics.The odds ratio (OR) reflects the correlation between diseases and exposure.A positive value indicates a positive correlation, whereas a negative value indicates a negative correlation.The size indicates the strength of the correlation between the two.The confidence interval (CI) is the estimated interval of the population parameters constructed using the sample statistics, and the CI in the table is the confidence interval of OR value.
Variables selected in the multivariate analysis were used as final predictors to establish a risk prediction model for the postoperative non-union of closed femoral shaft fractures presented as a nomogram.First, we performed internal validation using the bootstrap resampling process (n = 1000) in the training cohort, calculated the C-index, and drew a calibration curve to evaluate its predictive accuracy.Second, to assess its external validity, the discrimination and calibration of the model were determined by drawing ROC and calibration curves, calculating C-indices, and performing H-L tests.Furthermore, clinical effectiveness was evaluated using the DCA curve, and a net clinical benefit was obtained.

Study populations
As shown in Fig. 1, a total of 729 patients with closed femoral shaft fractures were enrolled in this study, and the comparison of sex and age of 729 included patients with 1024 excluded patients showed that all values were P > 0.05 (SI Table 1).617 patients were assigned to the training cohort and 112 patients to the external validation cohort, and followed up for 12-84 months (mean, 52.5 ± 20.0).There were 66 cases of postoperative femoral shaft fracture non-union, with a non-union rate of 9.1%.The mean age was 25.1 ± 17.2 years; the population included 554 men (76.0%) and 175 women (24.0%) with a male-to-female ratio of 3.2:1.The number of patients with closed femoral shaft fractures was the highest in the 0-10 years group, followed by the 21-30 years group.For patients aged > 30 years, the number of fractures gradually decreased with increasing age, and the proportion of male patients in each age group was higher (Fig. 2).

Model variable screening
Univariate analysis in the training cohort showed that patients affected by non-union had higher percentages of type B and C fractures, older age, bone defects, smoking, and postoperative infection than patients with closed femoral shaft fracture union (P < 0.05) (Table 1).These factors were included in the multivariate logistic regression analysis.

Model validation and nomogram construction
The C-indices were 0.818 (95% CI, 0.764-0.872) in the training cohort and 0.781 (95% CI, 0.652-0.910) in the external validation cohort, illustrating that the model had a medium level of discrimination.The internal validation also yielded a consistent conclusion, with a C-index of 0.804.ROC curves were constructed for the training cohort (Fig. 3A) and the validation cohort (Fig. 3B).
In the calibration plots (Fig. 4), the fitting curves of the model were close to the ideal curves, indicating that the model had considerable calibrating abilities.The H-L test showed a good fit of the model, with values of P = 0.902 in the training cohort and P = 0.476 in the validation cohort.
As shown in Fig. 5, according to the DCA curve, the best clinical effectiveness was achieved when the threshold probability was in the range of 0.10-0.40,and the net benefit of taking treatment measures was higher.A nomogram was used to visualize the results of the clinical prediction model (Fig. 6A).In practical applications, the risk of non-union of closed femoral shaft fractures can be determined based on relevant variables of the individual.For example, for patients with type B fractures, smokers, bone defects, and no postoperative infection, a corresponding score was obtained from the nomogram according to the value of each factor.The risk of non-union was 0.468 (Fig. 6B).

Discussion
The incidence of femoral shaft fractures is 2.1-18.4/100000 19 ; most cases are caused by high-energy injuries and often accompanied by fractures in other parts, such as the proximal femur 20 .If treatment is delayed or inappropriate, limb deformities and dysfunction can occur, seriously affecting patients' postoperative recovery and endangering their physical and mental health.Therefore, the prediction and screening of high-risk patients who will experience poor healing after femoral shaft fracture surgery and timely treatment measures can effectively improve recovery and reduce pain.In this study, a clinical predictive nomogram was developed and validated to predict the risk of postoperative non-union in patients with closed femoral shaft fractures.Using single-and multifactor analyses, we incorporated the selected variables into the model, and the model evaluation showed good discrimination, calibration, and clinical effectiveness.According to the nomogram, fracture classification was the most important predictor, followed by bone defect, smoking, and postoperative infection.This study found that complex fractures, namely wedge-shaped and comminuted fractures, was an independent risk factor for the postoperative non-union of closed femoral shaft fractures.Type B and C fractures are more serious; there are more free bone blocks at the broken end of the fracture, and postoperative stability is poor.In addition, to achieve anatomical reduction during surgery, the soft tissue is severely damaged and stripped, which destroys the local blood supply and causes insufficient perfusion 21 , thus causing poor bone healing.Santolini et al. 22 concluded that complex fractures and high initial fracture displacement increased the risk of non-union in long bone fractures.Similarly, Hung et al. 23 showed that the risk factors for non-union of femoral shaft fractures were types B and C according to AO/OTA classification, consistent with the results of this study.According to a study on the factors of non-union of shaft fractures by Jensen 24 , type B fractures have a more significant effect on non-union than type A fractures.Moreover, we found that bone defects increased the risk of postoperative non-union of femoral shaft fractures.Fracture healing is related to the contact area's proximity and size 25 .Bone defects reduce the contact area, resulting in difficult anatomical reduction of the broken end, difficult osteogenic bridging of osteoblasts, weak callus formation at the broken end, inability to form continuous callus, and thus bone non-union.Ru et al. 26 reported that fracture patients with bone defects ≥ 5 mm were more likely to develop  www.nature.com/scientificreports/non-union.Some found that if the bone defect does not exceed 50% of the bone perimeter, conventional fixation techniques can usually achieve self-healing and have a lower risk of bone non-union 27 .
In addition, smoking is an independent risk factor for the postoperative non-union of closed femoral shaft fractures.Studies have shown that smoking can interrupt chondrogenesis and cause abnormal activity in important repair cell groups, such as bone stem cells and progenitor cells 28 , thus inhibiting bone formation and mineralization, resulting in reduced mechanical stability 29 .Inhaled substances such as carbon monoxide and nicotine can reduce the oxygen-carrying capacity of blood and constrict blood vessels.This leads to decreased tissue oxygen content and blood supply 30 , which affects bone healing and increases the risk of bone non-union.In a study by Westgeest et al. 31 , smoking was significantly correlated with the development of non-union.Tian et al. 32 found that smoking is an influential factor in tibial fracture non-union.Hernigou and Schuind's 33 multivariate analysis of diaphyseal fractures showed that smoking was significantly correlated with non-union in both open and closed fractures; these findings are consistent with the results of this study.However, some scholars have concluded that there is no direct correlation between smoking and non-union 34,35 .
Postoperative infection also affects the healing of patients with closed femoral shaft fractures.According to statistics, 5% of bone non-union cases are related to infection 36 .Contamination by pathogenic bacteria leads to the persistent existence of neutrophils, which limits the recruitment of monocytes or macrophages and the differentiation of osteoblast progenitor cells and affects callus formation in the early stage of fracture healing 37 .Bacterial infection destroys the stable internal environment required for fracture healing and affects the formation and transformation of callus at the fracture site 38 .In a study by Hellwinkel 39 , infection was an important driver of non-union.Simpson and Tsang 40 reached similar conclusions.In an analysis of risk factors for nonunion of tibial fractures, Ford et al. 41 found that deep infection is an important predictor of non-union.Ross et al. 42 reported that infection within 6 weeks of surgery was related to fracture non-union.In addition, the local antibacterial treatment of fractures to eliminate infections reportedly can significantly improve bone healing and support fracture repair 43,44 .
It is worth noting that studies have shown that osteoporosis and diabetes are risk factors for fracture nonunion 45,46 ; however, the results of this study suggest the lack of a significant association, possibly due to the study population.These factors are mostly observed in elderly individuals, whereas femoral shaft fractures are mostly caused by high-energy injuries.Among the cases included in this study, most patients were young and middleaged and few had comorbid diseases such as diabetes and osteoporosis; therefore, there was no statistical difference in the results.However, some scholars reported that diabetes was confirmed as a risk factor for non-union only in retrospective studies involving the feet and ankles 47 ; thus, the risk of non-union of long bone fractures remains to be further explored.Mills et al. 48reported that an increased risk of non-union is related to male sex and a high BMI.Rodriguez et al. 49 studied the factors influencing distal femoral shaft fracture healing and found that obesity was a risk factor for non-union.Tsai et al. 50found that sex was not associated with fracture healing.Ku et al. 51 analyzed the risk factors for non-union in patients with distal humeral fractures after open reduction and internal fixation and found that BMI was not a statistically significant factor, a finding that is consistent with the results of this study.Cheng et al. 52 confirmed that serum albumin level affects fracture healing; however, we did not obtain similar results after including it.Owing to the different research groups, the elderly people have higher requirements for nutrition, while femoral shaft fractures tend to occur in young and middle-aged men.The nutritional status of this group recovers quickly, which may not be significantly related to fracture non-union.Some studies confirmed that proper weight-bearing activity after surgery can produce biomechanical stimulation at the fracture site, which shortens the healing time of femoral shaft fractures 53 .Taitsman et al. 54 showed that delayed weight loading increases the risk of non-union in femoral shaft fractures.In this study, postoperative weight-bearing was not related to fracture non-union.This may be because of the retrospective collection of fracture patients with a large time span that inevitably resulted in a certain recall deviation; therefore, the results are inconsistent with those of previous research.In addition, some scholars reported that the increased risk of non-union is related to smoking and alcoholism 55 , while Zura et al. 's 5 study of the epidemic trend and related factors of fracture non-union found no direct relationship between alcohol consumption and fracture non-union, similar to the conclusion of this study.
Our study had several limitations.First, its retrospective design means that information bias is inevitable, and detailed records, such as bone defect size and shape, classification of postoperative infection, and pathogenic bacteria, are insufficiently comprehensive.Second, as this was a single-center study, the ability to generalize our findings to patients in other regions is low, which affects the accuracy of the results.Furthermore, the sample is not representative, as young and middle-aged people accounted for the majority of the study population, which affects the analysis of age-related risk factors.Our findings require validation in future studies with larger sample sizes using a multicenter prospective approach to obtain data for a more comprehensive and accurate database.
In conclusion, complex fractures, bone defects, smoking, and postoperative infection are independent risk factors of closed femoral shaft fracture non-union.Combined with the nomogram, the postoperative prognosis of closed femoral shaft fractures can be predicted, which can guide orthopedic doctors in conducting preoperative examinations, surgical plans, and administering targeted rehabilitation training to guarantee the postoperative healing of femoral shaft fractures.

Figure 1 .
Figure 1.The screening process of research objects.

Figure 2 .
Figure 2. Sex and age distribution of patients with closed femoral shaft fracture.

Figure 3 .
Figure 3. ROC curve of the prediction model for postoperative non-union of closed femoral shaft fracture, (A) training cohort, (B) validation cohort.

Figure 4 .
Figure 4. Calibration curve of the prediction model for postoperative non-union of closed femoral shaft fracture, (A) training cohort, (B) internal validation cohort, (C) external validation cohort.

Figure 5 .
Figure 5. DCA curve of the prediction model for postoperative non-union of closed femoral shaft fracture, (A) training cohort, (B) validation cohort.

Figure 6 .
Figure 6.(A) Nomogram of the prediction model for postoperative non-union of closed femoral shaft fracture.(B) Schematic diagram of risk scoring on the nomogram.

Table 2 .
Multivariate logistic regression analysis results related to postoperative non-union of closed femoral shaft fracture.